package com.gxc.array;

/**
 *
 64. 最小路径和

 给定一个包含非负整数的 m x n 网格 grid ，请找出一条从左上角到右下角的路径，使得路径上的数字总和为最小。

 说明：每次只能向下或者向右移动一步
 */
public class MinPathSum {

    public static void main(String[] args) {
        System.out.println(handle(new int[][]{
                {1,3,1},{1,5,1},{4,2,1}
        }));
        System.out.println(handle2(new int[][]{
                {1,3,1},{1,5,1},{4,2,1}
        }));


        System.out.println(handle(new int[][]{
                {1,2,3},{4,5,6}
        }));
        System.out.println(handle2(new int[][]{
                {1,2,3},{4,5,6}
        }));
    }

    public static int handle(int[][] grid) {
        int m = grid.length;
        int n = grid[0].length;

        int[][] dp = new int[m][n];
        dp[0][0] = grid[0][0];
        for (int i = 1; i < m; i++) {
            dp[i][0] = grid[i][0] + dp[i-1][0];
        }
        for (int i = 1; i < n; i++) {
            dp[0][i] = dp[0][i-1] + grid[0][i];
        }

        for (int i = 1; i < m; i++) {
            for (int j = 1; j < n; j++) {
                dp[i][j] = grid[i][j] + Math.min(dp[i-1][j], dp[i][j-1]);
            }
        }

        return dp[m-1][n-1];
    }

    public static int handle2(int[][] grid) {
        int m = grid.length;
        int n = grid[0].length;

        int[] dp = new int[n];
        dp[0]=grid[0][0];
        for (int i = 1; i < n; i++) {
            dp[i] = dp[i-1] + grid[0][i];
        }

        for (int i = 1; i < m; i++) {
            for (int j = 0; j < n; j++) {
                if (j==0) {
                    dp[j] = grid[i][j] + dp[j];
                } else {
                    dp[j] = grid[i][j] + Math.min(dp[j-1], dp[j]);
                }
            }
        }
        return dp[n-1];
    }
}
